Pick any exercise in Chapter 12 of the calculus textbook. Post the solution or your attempt. Discuss any issues you might have had.
What were the most valuable elements you took away from this course?
Evaluate \(f_x(x, y)\) and \(f_y(x, y)\) at the indicated point.
\[f(x,y) = x^3 − 3x + y^2 − 6y\ at\ (−1,3)\]
\[f_x(x,y) = 3x^2 − 3\] \[f_x(-1,3) = 3(-1)^2 − 3\]
\[f_x(-1,3) = 0\]
\[f_y(x,y) = 2y − 6\]
\[f_y(-1,3) = 2(3) − 6\] \[f_y(-1,3) = 0\]
f_ <- expression(x**3 - 3*x + y**2 - 6*y)
x <- -1
y <- 3
f_x <- D(f_, "x")
f_x## 3 * x^2 - 3f_y <- D(f_, "y")
f_y## 2 * y - 6eval(f_x)## [1] 0eval(f_y)## [1] 0